Example of How the Fed Uses an Open Market Purchase to Increase the Money Supply in a Fractional Reserve Banking System with 10% Required Reserves

Example of How the Fed Uses an Open Market Purchase to Increase the Money Supply in a Fractional Reserve Banking System with 10% Required Reserves

Suppose the Fed conducts an open market purchase of a $1000 Treasury bill from a securities dealer, Adam Aardvark, with a checking account at the First National Bank. What would be the total effect on the money supply?

To examine changes in the balance sheets of banks, economists use T-accounts. A T-account is a simplified balance sheet with lines in the form of a T that lists only the changes that occur in the balance sheet items from some initial balance sheet position.

For simplicity, assume all banks have the same initial balance sheet as illustrated in the sample above for the First National Bank.

Assume the required reserve ratio is 10% (rr = .10) and banks do not hold any additional excess reserves. If banks hold more reserves than required, the reserve ratio, R, is larger than the required reserve ratio, rr. If banks do not hold excess reserves, however, the reserve ratio is equal to the required reserve ratio (R = rr). This implies banks will make loans for the maximum amount of any new deposits. When the Fed purchases the $1000 government security from Adam Aardvark (who has an account at the First National Bank), the bank’s balance sheet changes as follows:


Table 17.
Changes in the Balance Sheet of the FIRST NATIONAL BANK
Assets
Liabilities & Net Worth
Reserves
+ $1000
Deposits
(Adam’s account)
+ $1000



Table 18.
Balance Sheet of the First National Bank
Assets
Liabilities & Net Worth
Reserves
(required = $ 1,000,100)
(excess = $ 400,900)
$1,401,000
Deposits
$10,001,000
Loans
$7,500,000


Government Securities
$900,000


Property & other assets
$600,000
Net Worth
$400,000




Total Assets
$10,401,000
Total Liabilities
& Net Worth
$10,401,000

When the Fed conducts the open market purchase of the $1000 government security, the Fed has credited $1000 to the First National Bank’s account at the Fed. This increases the First National Bank’s reserves. Its reserves are the sum of the currency in the First National Bank’s vault plus the balance in the First National Bank’s account at the Federal Reserve. The First National Bank, in turn, credits $1000 to the securities dealer’s account at the First National Bank. The open market operation has increased the assets of the First National Bank by $1000 (the increase in its reserves) and has increased the liabilities of the First National Bank by $1000 (the additional $1000 deposited in Adam Aardvark’s account).

Since it is assumed banks do not want to hold any additional excess reserves, the First National Bank will keep only the required amount of reserves and will loan out the additional reserves in order to earn additional interest income. Since the required reserve ratio is .10, the First National Bank will be required to keep 10 percent of this additional deposit as reserves. Since the new deposit in the securities dealer’s account is $1000, the First National Bank is required to keep $100 of it as reserves and can create $900 in loans.


Table 19.
Changes in the Balance Sheet of the FIRST NATIONAL BANK
Assets
Liabilities & Net Worth
Loans
+ $900
Deposits
+ $900


Table 20.
Balance Sheet of the First National Bank
Assets
Liabilities & Net Worth
Reserves
(required = $ 1,000,190)
(excess = $ 400,810)
$1,401,000
Deposits
$10,001,900
Loans
$7,500,900


Government Securities
$900,000


Property & other assets
$600,000
Net Worth
$400,000




Total Assets
$10,401,900
Total Liabilities
& Net Worth
$10,401,900


Suppose the First National Bank loans the $900 to Bernice Bear. It does this by increasing the balance in Bernice’s checking account at First National Bank. The money supply has just increased by another $900. (Remember the M1 definition of the money supply is currency in circulation plus the balances in checking accounts plus travelers’ checks outstanding.) The total effect on the money supply to this point is $1900. The securities dealer, Adam Aardvark, still has the $1000 increase in his account (deposits) and Bernice Bear has the $900 increase in her account.

When people borrow money, they usually spend it right away. Suppose Bernice buys a $900 painting from Charlie Cheetah. Suppose Charlie deposits this in his bank, Second National Bank. Bernice’s account balance at First National Bank decreases by $900 and Charlie’s account balance at Second National Bank increases by $900. One of the Fed’s functions is to clear checks in the banking system. In this case, the check is cleared when the Fed deducts $900 from the First National Bank’s account at the Fed and adds $900 to the Second National Bank’s account at the Fed. Notice that the First National Bank’s reserves decrease by $900 and the Second National Bank’s reserves increase by $900. The total amount of reserves in the banking system remains unchanged, however.


Table 21.
Changes in the Balance Sheet of the FIRST NATIONAL BANK
Assets
Liabilities & Net Worth
Reserves
- $900
Deposits
- $900


Table 22.
Balance Sheet of the First National Bank
Assets
Liabilities & Net Worth
Reserves
(required = $ 1,000,100)
(excess = $ 400,000)
$1,400,100
Deposits
$10,001,000
Loans
$7,500,900


Government Securities
$900,000


Property & other assets
$600,000
Net Worth
$400,000




Total Assets
$10,401,000
Total Liabilities
& Net Worth
$10,401,000

Table 23.
Changes in the Balance Sheet of the SECOND NATIONAL BANK
Assets
Liabilities & Net Worth
Reserves
+ $900
Deposits
+ $900

Table 24.
Balance Sheet of the Second National Bank
Assets
Liabilities & Net Worth
Reserves
(required = $ 1,000,090)
(excess = $ 400,810)
$1,400,900
Deposits
$10,000,900
Loans
$7,500,000


Government Securities
$900,000


Property & other assets
$600,000
Net Worth
$400,000




Total Assets
$10,400,900
Total Liabilities
& Net Worth
$10,400,900

The total change in the money supply to this point is still $1900. Adam still has the additional $1000 in his account at First National Bank and Charlie now has an additional $900 in his account at Second National Bank.

With Charlie’s $900 deposit, the Second National Bank also has a $900 increase in its reserves. The bank is only required to keep 10% of deposits as reserves and it is assumed banks do not hold any additional excess reserves. Thus, the Second National Bank will keep $90 of the new deposit as reserves and will create $810 in new loans.

Table 25.
Changes in the Balance Sheet of the SECOND NATIONAL BANK
Assets
Liabilities & Net Worth
Loans
+ $810
Deposits
+ $810


Table 26.
Balance Sheet of the Second National Bank
Assets
Liabilities & Net Worth
Reserves
(required = $ 1,000,171)
(excess = $ 400,729)
$1,400,900
Deposits
$10,001,710
Loans
$7,500,810


Government Securities
$900,000


Property & other assets
$600,000
Net Worth
$400,000




Total Assets
$10,401,710
Total Liabilities
& Net Worth
$10,401,710


Suppose Second National Bank loans $810 to Dino Dolphin and increases his account balance by $810. The creation of this loan will increase the money supply by an additional $810. The total effect on the money supply so far is $2710. Adam still has the $1000 increase in his account at the First National Bank, Charlie still has the $900 increase in his account at the Second National Bank, and Dino now has a $810 increase in his account at the Second National Bank. ($1000 + $900 + $810 = $2710.)

Suppose Dino uses the $810 to buy a decorative ceramic bowl from Esmeralda Elephant. Suppose Esmeralda deposits the $810 in her account at the Third National Bank. Dino’s account balance at the Second National Bank decreases by $810 and Esmeralda’s account balance at the Third National Bank increases by $810.

When the Fed clears this check, it deducts $810 from the Second National Bank’s account at the Fed and adds $810 to the Third National Bank’s account at the Fed. Notice that the Second National Bank’s reserves decrease by $810 and the Third National Bank’s reserves increase by $810. The total amount of reserves in the banking system remains unchanged.


Table 27.
Changes in the Balance Sheet of the SECOND NATIONAL BANK
Assets
Liabilities & Net Worth
Reserves
- $810
Deposits
- $810


Table 28.
Balance Sheet of the Second National Bank
Assets
Liabilities & Net Worth
Reserves
(required = $ 1,000,090)
(excess = $ 400,000)
$1,400,090
Deposits
$10,000,900
Loans
$7,500,000


Government Securities
$900,000


Property & other assets
$600,000
Net Worth
$400,000




Total Assets
$10,401,710
Total Liabilities
& Net Worth
$10,400,900

Table 29.
Changes in the Balance Sheet of the THIRD NATIONAL BANK
Assets
Liabilities & Net Worth
Reserves
+ $810
Deposits
+ $810

Table 30.
Balance Sheet of the Third National Bank
Assets
Liabilities & Net Worth
Reserves
(required = $ 1,000,090)
(excess = $ 400,810)
$1,400,810
Deposits
$10,000,810
Loans
$7,500,000


Government Securities
$900,000


Property & other assets
$600,000
Net Worth
$400,000




Total Assets
$10,400,810
Total Liabilities
& Net Worth
$10,400,810

The total change in the money supply is still $2710. Adam still has the $1000 increase in his account at the First National Bank, Charlie still has the $900 increase in his account at the Second National Bank, and Esmeralda now has a $810 increase in her account at the Third National Bank. ($1000 + $900 + $810 = $2710.)

The Third National Bank is required to keep 10% of this new deposit as reserves and can loan out the rest. This means the Third National Bank will keep $81 of reserves and will create $729 of new loans.

Table 31.
Changes in the Balance Sheet of the THIRD NATIONAL BANK
Assets
Liabilities & Net Worth
Loans
+ $729
Deposits
+ $729





Table 32.
Balance Sheet of the Third National Bank
Assets
Liabilities & Net Worth
Reserves
(required = $ 1,000,090)
(excess = $ 400,810)
$1,400,810
Deposits
$10,001,539
Loans
$7,500,729


Government Securities
$ 900,000


Property & other assets
$600,000
Net Worth
$ 400,000




Total Assets
$10,401,539
Total Liabilities
& Net Worth
$10,401,539


Suppose the Third National Bank loans $729 to Francesca Ferret. Francesca’s account balance at the Third National Bank increases by $729. The total increase in the money supply at this point is now $3439. Adam still has the $1000 increase in his account at the First National Bank, Charlie still has the $900 increase in his account at the Second National Bank, Esmeralda still has the $810 increase in her account at the Third National Bank, and Francesca now has a $729 increase in her account balance at the Third National Bank. ($1000 + $900 + $810 + $729 = $3439.)

Suppose Francesca uses the $729 to buy a tapestry from Gary Gorilla. Suppose Gary deposits the $729 in his bank, the Fourth National Bank. Francesca’s account balance at the Third National Bank decreases by $729 and Gary’s account balance at the Fourth National Bank increases by $729.

The total change in the money supply is still $3439. Adam still has the $1000 increase in his account at the First National Bank, Charlie still has the $900 increase in his account at the Second National Bank, and Esmeralda still has the $810 increase in her account at the Third National Bank and Gary now has a $729 increase in his account at the Fourth National Bank. ($1000 + $900 + $810 + $729 = $3439.)

The Fourth National Bank is required to keep 10% of this new deposit as reserves and can loan out the rest. This means the Fourth National Bank will keep $72.90 of reserves and will create $656.10 of new loans.

Table 33.
FOURTH NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves + $81
Deposits + $810
Excess Reserves

Loans + $729
Net Worth
Government Securities

Property & other assets


Suppose Fourth National Bank loans $656.10 to Gary Gorilla. Gary uses the money to buy a sculpture from Helen Hyena. Suppose Helen deposits the $656.10 in her bank, Fifth National Bank.

This bank will be required to keep 10% of this deposit as reserves and will loan out the rest. This means the Fifth National Bank will increase its required reserves by $72.90 and will increase its loans by $656.10.

Table 34.
FIFTH NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves + $72.90
Deposits + $729
Excess Reserves

Loans + $656.10
Net Worth
Government Securities

Property & other assets


Suppose Fifth National Bank loans $656.10 to Ian Impala. Ian uses the money to buy a hand-made rug from Julius Jaguar. Julius now has $656.10 that he did not have before. Suppose Julius deposits the $656.10 in his bank, Sixth National Bank. This bank will be required to keep 10% of this deposit as reserves and will loan out the rest. This means the Sixth National Bank will increase its required reserves by $65.61 and will increase its loans by $590.49.

Table 35.
SIXTH NATIONAL BANK
ASSETS
LIABILITIES & NET WORTH
Required Reserves + $65.61
Deposits + $656.10
Excess Reserves

Loans + $590.49
Net Worth
Government Securities

Property & other assets


The open market purchase of a $1000 government security from the First National Bank has caused an increase in the money supply that is much larger than $1000. So far, the money supply has increased by $4095.10.

Bernice Bear still has the additional $1000 in her account at the Second National Bank, Diego Dolphin still has the additional $900 in his account at Third National Bank, Francesca Ferret still has the additional $810 in her account at the Fourth National Bank, Helen Hyena still has the additional $729 in her account at the Fifth National Bank, and Julius Jaguar still has the additional $656.10 in his account at the Sixth National Bank. The additions to people’s checking accounts are $1000 + $900 + $810 + $729 + $656.10 = $4095.10. This process could continue, however. Eventually the total increase in the money supply would be $10,000. The amount of money the banking system generates with each dollar of reserves is the money multiplier. The money multiplier is the inverse of the reserve ratio. In this example, the reserve ratio is .10. Thus the money multiplier is 1/.10 = 10. Thus, each dollar of reserves generates $10 of money. Since the open market operation increased reserves by $1000, the total effect on the money supply is 10 times $1000 = $10,000.

If we continued this example, new loans would be created and deposited, creating new loans to be deposited, creating new loans, etc.
So what is the total effect on the money supply?

The increase in the money supply from a $1000 increase in the reserves when the reserve ratio is 10% and banks loan out all additional excess reserves is:

Change in money supply = 1000 + $900 + $810 + $729 + $656.10 + . . . + . . . + . . . = $10,000.

The formula for making this calculation is:

Increase in reserves / reserve ratio = total increase in the money supply

or

$1000 / .10 = $10,000